Analyze the music to identify where the melody exists. The melody will usually be the highest-pitched part in the music. Remove chords and arpeggios from the music. You won't be able to play chords and arpeggios with just one hand. Isolate the melodic elements to make it easier to play the music.
Use a sheet of staff paper to write out the melodic elements that you can play with one hand. This may take some experimentation. Remember that you should use only the most memorable parts of the song. Because a good melody infers chord progressions, you can leave the chords out and concentrate on writing a melody that makes sense. After writing the melody, go back and see if you can add any reinforcing elements, such as an interval, or a small musical motive to the piece.
Learn how to number fingers to play just the melody of the music. The fingerings used will depend on the hand that you have available. Starting with the thumbs, move outward. Write the thumbs as one, the index fingers as two, the middle fingers as three, the ring fingers as four and the pinkies as five. Using the same fingers will help your muscles to develop muscle-memory to make it easier to play. With muscle-memory, your fingers learn patterns so that you don't have to think about every note.
Place your usable hand on the piano and begin to practice the melody that you have written. You must use the same fingerings each time or your fingers will not learn the correct patterns and playing the piece with one hand will be difficult. Practice no more than one measure of music at a time until you have perfected that measure. When playing, aim for a smooth and connected technique by holding each note the full value.